What is the difference between a distribution and a process (Poisson)? I'm doing my PhD in geomechanics. I thought we use a Poisson-Weibull distribution (for the variability of a parameter at the rock), but reading more about the subject I think maybe is a Poisson-Weibull process and I don't know the difference. To complete the problem I'm not too knowledgeable about the language of mathematics, so if you could give me an example it would be awesome!
 A: *

*Poisson distribution = a specific  discrete probability distribution, i.e. a  probability distribution characterized by a probability mass function. Specifically, in the case of Poisson, it is defined as $P(k \text{ events in interval}) = \frac{\lambda^k e^{-\lambda}}{k!}$, $\lambda \in \mathbb{R^+}, k \in \mathbb{N}$.

*Poisson process = a  stochastic process, i.e.  a collection of random variables representing the evolution of some system of random values over time. In other words,  it is a family of real random variables $(X_t)_{t\in T}$ defined on a probability space $(\Omega,\Sigma,P)\ ,$ where the set T is interpreted as ''time''. Specifically, a Poisson process can be defined in different ways, not necessarily using the Poisson distribution:



A: A random process is a sequence of random variables. That means, when talking about a process, e.g. Poisson process, an element of occurrences as a sequence in time is involved, while when we talk about random variables and their distribution, e.g. Poisson distribution, there is no such element involved, and we only have a random variable X with its associated distribution. 
Example: 
Random variable X: the number of phone calls to a receptionist per hour follows the Poisson distribution (and with the distribution known we can have the probability of receiving a certain number of phone calls in a given time interval); 
Random process {X1, X2, ....}, where Xi: the time when the ith phone call was received, is a Poisson process.
